Boundary value problems modeling moisture transport in soils

To model the moisture transport in soil and to better understand physics underneath, we study a boundary value problem for a nonlinear hyperbolic PDE. Using a constructive method for approximation of solutions of the problem, we derive sufficient conditions for existence and uniqueness of its regular solutions and show that these solutions satisfy the sign-preserving inequalities. Additionally, we prove a comparison theorem and a theorem about differential inequalities, and derive an posteriori error of the method. Theoretical results are validated on an illustrative numerical example.